Mathematics Solutions Solutions for Class 8 Math Chapter 1 Rational And Irrational Numbers are provided here with simple step-by-step explanations. These solutions for Rational And Irrational Numbers are extremely popular among Class 8 students for Math Rational And Irrational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 8 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

#### Page No 55:

#### Question 1:

If marked price = ₹1700, selling price = ₹1540 then find the discount.

#### Answer:

Marked price = ₹ 1,700

Selling price = ₹ 1,540

∴ Discount = Marked price − Selling price = ₹ 1,700 − ₹ 1,540 = ₹ 160

#### Page No 55:

#### Question 2:

If marked price = ₹990 and percentage of discount is 10, then find the selling price.

#### Answer:

10% discount is given on the marked price. Therefore, if marked price is ₹ 100, then selling price is ₹ 90.

Let the selling price be ₹ *x *when the marked price is ₹ 990.

$\therefore \frac{x}{990}=\frac{90}{100}$

$\Rightarrow x=\frac{90}{100}\times 990$ = ₹ 891

Thus, the selling price is ₹ 891.

#### Page No 55:

#### Question 3:

If selling price = ₹900. Discount is 20%, then find the marked price.

#### Answer:

20% discount is given on the marked price. Therefore, if marked price is ₹ 100, then selling price is ₹ 80.

Let the marked price be ₹ *x *when the selling price is ₹ 900.

$\therefore \frac{900}{x}=\frac{80}{100}$

$\Rightarrow x=\frac{100}{80}\times 900$ = ₹ 1,125

Thus, the marked price is ₹ 1,125.

#### Page No 55:

#### Question 4:

The marked price of the fan is 3000 rupees. Shopkeeper gave 12% discount on it. Find the total discount and selling price of the fan.

#### Answer:

12% discount is given on the marked price. Therefore, if marked price is ₹ 100, then selling price is ₹ 88.

Let the selling price be ₹ *x *when the marked price is ₹ 3,000.

$\therefore \frac{x}{3000}=\frac{88}{100}$

$\Rightarrow x=\frac{88}{100}\times 3000$ = ₹ 2,640

So, the selling price of the fan is ₹ 2,640.

∴ Discount = Marked price − Selling price = ₹ 3,000 − ₹ 2,640 = ₹ 360

Thus, the discount on fan is ₹ 360.

#### Page No 55:

#### Question 5:

The marked price of a mixer is 2300 rupees. A customer purchased it for Rs. 1955. Find percentage of discount offered to the customer.

#### Answer:

Marked price of the mixer = ₹ 2,300

Selling price of the mixer = ₹ 1,955

∴ Discount = Marked price − Selling price = ₹ 2,300 − ₹ 1,955 = ₹ 345

On marked price of ₹ 2,300, the discount is ₹ 345.

Let the discount be ₹ *x*.

Now, if the marked price is ₹ 100, then the discount is ₹ *x*.

∴ $\frac{x}{100}=\frac{345}{2300}$

⇒ $x=\frac{345}{2300}\times 100$ = 15

Thus, the percentage of discount offered to the customer is 15%.

#### Page No 55:

#### Question 6:

A shopkeeper gives 11% discount on a television set, hence the cost price of it is Rs. 22,250. Then find the marked price of the television set.

#### Answer:

Let the marked price of the television set be Rs *x*.

Discount percent on the television set = 11%

If the marked price of the television set was Rs 100, then the customer would have paid (Rs 100 − Rs 11) Rs 89 for the television set.

It is given that cost price of the television set to the customer is Rs 22,250.

∴ $\frac{89}{100}=\frac{22250}{x}$

⇒ $x=22250\times \frac{100}{89}$ = Rs 25,000

Thus, the marked price of the television set is Rs 25,000.

#### Page No 55:

#### Question 7:

After offering discount of 10% on marked price, a customer gets total discount of 17 rupees. To find the cost price for the customer, fill in the following boxes with appropriate numbers and complete the activity.

Suppose, marked price of the item = 100 rupees

Therefore, for customer that item costs $\overline{){0}}-\overline{){0}}$ = 90 rupees

Hence, when the discount is $\overline{){0}}$ then the selling price is $\overline{){0}}$ rupees.

Suppose when the discount is $\overline{){0}}$ rupees, the selling price is *x* rupees.

$\therefore \frac{x}{\overline{){0}}}=\frac{\overline{){0}}}{\overline{){0}}}\therefore x=\frac{\overline{){0}}\times \overline{){0}}}{\overline{){0}}}=\overline{){0}}$

∴ the customer will get the item for 153 rupees.

#### Answer:

Suppose, marked price of the item = 100 rupees

Therefore, for customer that item costs $\overline{)100}-\overline{)10}$ = 90 rupees

Hence, when the discount is $\overline{)10}$ then the selling price is $\overline{)90}$ rupees.

Suppose when the discount is $\overline{)17}$ rupees, the selling price is *x* rupees.

$\therefore \frac{x}{\overline{)17}}=\frac{\overline{)90}}{\overline{)10}}\therefore x=\frac{\overline{)90}\times \overline{)17}}{\overline{)10}}=\overline{)153}$

∴ the customer will get the item for 153 rupees.

#### Page No 55:

#### Question 8:

A shopkeeper decides to sell a certain item at a certain price. He tags the price on the item by increasing the decided price by 25%. While selling the item, he offers 20% discount. Find how many more or less percent he gets on the decided price.

#### Answer:

Let the decided price of the item be ₹ 100.

∴ Marked price of the item = ₹ 100 + 25% of ₹ 100 = ₹ 100 + ₹ 25 = ₹ 125

Discount on the item = 20% of ₹ 125 = $\frac{20}{100}\times 125$ = ₹ 25

∴ Selling price of the item = Marked price of the item − Discount on the item = ₹ 125 − ₹ 25 = ₹ 100

Since the decided price of the item is same as the selling price of the item so the shopkeeper neither makes any profit nor any loss on selling the item.

Thus, the shopkeeper gets 0% on the decided price.

#### Page No 57:

#### Question 1:

John sold books worth rupees 4500 for a publisher. For this he received 15% commission. Complete the following activity to find the total commission John obtained.

Selling price of books = $\overline{){}{}{0}{}}$

Rate of commission = $\overline{){}{}{0}{}}$

Commission obtained = $\frac{\overline{){0}}}{\overline{){0}}}\times \overline{){0}}$

∴ Commission = $\overline{){}{}{0}{}}$ rupees.

#### Answer:

Selling price of books = $\overline{)4500}$ rupees

Rate of commission = $\overline{)15\%}$

Commission obtained = $\frac{\overline{)15}}{\overline{)100}}\times \overline{)4500}$ = Rs 675

∴ Commission = $\overline{)675}$ rupees

#### Page No 57:

#### Question 2:

Rafique sold flowers worth ₹ 15,000 by giving 4% commission to the agent. Find the commission he paid. Find the amount received by Rafique.

#### Answer:

Selling price of the flowers = ₹ 15,000

Commission rate = 4%

Commission paid to the agent = 4% of ₹ 15,000 = $\frac{4}{100}\times 15000$ = ₹ 600

So, the commission paid by Rafique is ₹ 600.

∴ Amount received by the Rafique

= Selling price of the flowers − Commission paid to the agent

= ₹ 15,000 − ₹ 600

= ₹ 14,400

Thus, the amount received by Rafique is ₹ 14,400.

#### Page No 57:

#### Question 3:

A farmer sold foodgrains for 9200 rupees through an agent. The rate of commission was 2%. How much amount did the agent get?

#### Answer:

Selling price of the foodgrains = ₹ 9,200

Commission rate = 2%

∴ Commission paid to the agent = 2% of ₹ 9,200 = $\frac{2}{100}\times 9200$ = ₹ 184

Thus, the commission received by the agent is ₹ 184.

#### Page No 58:

#### Question 4:

Umatai purchased following items from a Khadi-Bhandar.

(i) 3 sarees for 560 rupees each.

(ii) 6 bottles of honey for 90 rupees each.

On the purchase, she received a rebate of 12% . How much total amount did Umatai pay?

#### Answer:

Cost of each saree = Rs 560

∴ Cost of 3 sarees = 3 × 560 = Rs 1,680

Cost of each bottle of honey = Rs 90

∴ Cost of 6 bottles of honey = 6 × 90 = Rs 540

Total cost of the items purchased = Rs 1,680 + Rs 540 = Rs 2,220

Total rebate received = 12% of Rs 2,220 = $\frac{12}{100}\times 2220$ = Rs 266.40

∴ Total amount paid by Umatai

= Total cost of the items purchased − Total rebate received

= Rs 2,220 − Rs 266.40

= Rs 1,953.60

Thus, the total amount paid by Umatai is Rs 1,953.60.

#### Page No 58:

#### Question 5:

Use the given information and fill in the boxes with suitable numbers. Smt. Deepanjali purchased a house for ₹7,50,000 from Smt. Leelaben through an agent. Agent has charged 2% brokerage from both of them.

(1) Smt. Deepanjali paid $\overline{){0}}\times \frac{\overline{){0}}}{\overline{){0}}}$ = ₹ $\overline{){0}}$ brokerage for purchasing the house.

(2) Smt. Leelaben paid brokerage of ₹ $\overline{){0}}$

(3) Total brokerage received by the agent is ₹ $\overline{){0}}$

(4) The cost of house Smt. Deepanjali paid is ₹ $\overline{){0}}$

(5) The selling price of house for Smt. Leelaben is ₹ $\overline{){0}}$.

#### Answer:

(1) Smt. Deepanjali paid $\overline{)750000}\times \frac{\overline{)2}}{\overline{)100}}$ = ₹ $\overline{)15,000}$ brokerage for purchasing the house.

(2) Smt. Leelaben paid brokerage of ₹ $\overline{)15,000}$.

(3) Total brokerage received by the agent is ₹ 15,000 + ₹ 15,000 = ₹ $\overline{)30,000}$.

(4) The cost of house Smt. Deepanjali paid is ₹ 7,50,000 + ₹ 15,000 = ₹ $\overline{)7,65,000}$.

(5) The selling price of house for Smt. Leelaben is ₹ 7,50,000 − ₹ 15,000 = ₹ $\overline{)7,35,000}$.

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